Question

Racionalização! Alguém sabe me explicar?

Answer 1

$\frac{\sqrt{500}-3\sqrt{20}+2-2\sqrt5}{\sqrt5-1}=\frac{10\sqrt5-6\sqrt5+2-2\sqrt5}{\sqrt5-1}=\\ \\ \frac{2\sqrt5+2}{\sqrt5-1}*\frac{\sqrt5+1}{\sqrt5+1}=\frac{10+2\sqrt5+2\sqrt5+2}{4}=\\ \\ \frac{4\sqrt5+12}{4}=\sqrt5+3\\ \\ a=3 \ b=1 \ e \ c=5\\ \\ \boxed{a+b+c=9}$